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XGRouter: high-quality global router in X-architecture with particle swarm optimization

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Abstract

This paper presents a high-quality very large scale integration (VLSI) global router in X-architecture, called XGRouter, that heavily relies on integer linear programming (ILP) techniques, partition strategy and particle swarm optimization (PSO). A new ILP formulation, which can achieve more uniform routing solution than other formulations and can be effectively solved by the proposed PSO is proposed. To effectively use the new ILP formulation, a partition strategy that decomposes a large-sized problem into some small-sized sub-problems is adopted and the routing region is extended progressively from the most congested region. In the post-processing stage of XGRouter, maze routing based on new routing edge cost is designed to further optimize the total wire length and mantain the congestion uniformity. To our best knowledge, XGRouter is the first work to use a concurrent algorithm to solve the global routing problem in X-architecture. Experimental results show that XGRouter can produce solutions of higher quality than other global routers. And, like several state-of-the-art global routers, XGRouter has no overflow.

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References

  1. Chang Y J, Lee Y T, Gao J R, Wu P C, Wang T C. NTHU-route 2.0: a robust global router for modern designs. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 2010, 29(12): 1931–1944

    Article  Google Scholar 

  2. Roy J A, Markov I L. High-performance routing at the nanometer scale. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 2008, 27(6): 1066–1077

    Article  Google Scholar 

  3. Zhang Y, Xu Y, Chu C. FastRoute3.0: a fast and high quality global router based on virtual capacity. In: Proceedings of the 2008 IEEE/ACM International Conference on Computer-Aided Design. 2008, 344–349

    Chapter  Google Scholar 

  4. Dai K R, Liu W H, Li Y L. NCTU-GR: efficient simulated evolutionbased rerouting and congestion-relaxed layer assignment on 3-D global routing. IEEE Transactions on Very Large Scale Integration Systems, 2012, 20(3): 459–472

    Article  Google Scholar 

  5. Moffitt M D. Maizerouter: engineering an effective global router. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 2008, 27(11): 2017–2026

    Article  Google Scholar 

  6. Ao J, Dong S, Chen S, Goto S. Delay-driven layer assignment in global routing under multi-tier interconnect structure. In: Proceedings of the 2013 ACM International Symposium on International Symposium on Physical Design. 2013, 101–107

    Chapter  Google Scholar 

  7. Ozdal M M, Wong M D F. Archer: a history-based global routing algorithm. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 2009, 28(4): 528–540

    Article  Google Scholar 

  8. Liu W H, Kao W C, Li Y L, Chao K Y. NCTU-GR 2.0: multithreaded collision-aware global routing with bounded-length maze routing. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 2013, 32(5):709–722

    Article  Google Scholar 

  9. Cho M, Pan D Z. BoxRouter: a new global router based on box expansion and progressive ILP. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 2007, 26(12): 2130–2143

    Article  Google Scholar 

  10. Albrecht C. Global routing by new approximation algorithms for multicommodity flow. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 2001, 20(5): 622–632

    Article  Google Scholar 

  11. Hu J, Roy J A, Markov I L. Sidewinder: a scalable ILP-based router. In: Proceedings of ACM International Workshop on System Level Interconnect Prediction. 2008, 73–80

    Chapter  Google Scholar 

  12. Cho M, Lu K, Yuan K, Pan D Z. BoxRouter 2.0: a hybrid and robust global router with layer assignment for routability. ACM Transactions on Design Automation of Electronic Systems, 2009, 14(2): 32

    Article  Google Scholar 

  13. Vannelli A. An interior point method for solving the global routing problem. In: Proceedings of the IEEE 1989 Custom Integrated Circuits Conference. 1989, 1–4

    Google Scholar 

  14. Behjat L, Chiang A, Rakai L, Li J H. An effective congestion-based integer programming model for VLSI global routing. In: Proceedings of Canadian Conference on Electrical and Computer Engineering. 2008, 931–936

    Google Scholar 

  15. Behjat L, Vannelli A, Rosehart W. Integer linear programming models for global routing. INFORMS Journal on Computing, 2006, 18(2): 137–150

    Article  MathSciNet  MATH  Google Scholar 

  16. Wu T H, Davoodi A, Linderoth J T. GRIP: global routing via integer programming. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 2011, 30(1): 72–84

    Article  Google Scholar 

  17. Han Y, Ancajas D M, Chakraborty K, Roy S. Exploring highthroughput computing paradigm for global routing. IEEE Transactions on Very Large Scale Integration Systems, 2014, 22(1): 155–167

    Article  Google Scholar 

  18. Liu G G, Chen G L, Guo W Z. DPSO based octagonal steiner tree algorithm for VLSI routing. In: Proceedings of the 15th IEEE International Conference on Advanced Computational Intellligence. 2012, 383–387

    Google Scholar 

  19. Dong J, Zhu H L, Xie M, Zeng X. Graph Steiner tree construction and its routing applications. In: Proceedings of the 10th IEEE International Conference on ASIC. 2013, 1–4

    Google Scholar 

  20. Hung J H, Yeh Y K, Lin Y C, Huang H H, Hsieh T M. ECO-aware obstacle-avoiding routing tree algorithm. WSEAS Transactions on Circuits and Systems, 2010, 9(9): 567–576

    Google Scholar 

  21. Tsai C C, Kuo C C, Lee T Y. High performance buffered X-architecture zero-skew clock tree construction with via delay consideration. International Journal of Innovative Computing, Information and Control, 2011, 7(9): 5145–5161

    Google Scholar 

  22. Tsai C C, Kuo C C, Hsu F T, Lee T Y. Discharge-path-based antenn aeffect detection and fixing for X-architecture clock tree. Integration, the VLSI Journal, 2012, 45(1): 76–90

    Article  Google Scholar 

  23. Liu G G, Guo W Z, Niu Y Z, Chen G L, Huang X. A PSO-basedtiming- driven octilinear Steiner tree algorithm for VLSI routing considering bend reduction. Soft Computing, 2014, 19(5): 1153–1169

    Article  Google Scholar 

  24. Ho T Y. A performance-driven multilevel framework for the X-based full-chip router. Integrated circuit and system design. Power and timing modeling, optimization and simulation. Springer Berlin Heidelberg, 2009: 209–218

    Chapter  Google Scholar 

  25. Hu Y, Jing T, Hong X, Hu X, Yan G. A routing paradigm with novel resources estimation and routability models for X-architecture based physical design. Embedded computer systems: architectures, modeling, and simulation. Springer Berlin Heidelberg, 2005: 344–353

    Chapter  Google Scholar 

  26. Cao Z, Jing T, Hu Y, Shi Y, Hong X, Hu X, Yan G. DraXRouter: global routing in X-architecture with dynamic resource assignment. In: Proceedings of the 2006 Asia and South Pacific Design Automation Conference. 2006, 618–623

    Chapter  Google Scholar 

  27. Ho T Y. A performance-driven X-architecture router based on a novel multilevel framework. Integration, the VLSI Journal, 2009, 42: 400–408

    Article  Google Scholar 

  28. Teig S L. The X architecture: not your father’s diagonal wiring. In: Proceedings of ACM International Workshop on System-Level Interconnect Prediction. 2002, 33–37

    Google Scholar 

  29. Eberhar R C, Kennedy J. A new optimizer using particles swarm theory. In: Proceedings of the 6th International Symposium on Micro Machine and Human Science. 1995, 39–43

    Chapter  Google Scholar 

  30. Neumann F, Witt C. Bioinspired computation in combinatorial optimization: algorithms and their computational complexity. Springer, 2010

    Book  Google Scholar 

  31. Zhang Y, Gong D W. Generating test data for both paths coverage and faults detection using genetic algorithms: multi-path case. Frontiers of Computer Science, 2014, 8(5): 726–740

    Article  MathSciNet  Google Scholar 

  32. Rabanal P, Rodríguez I, Rubio F. An ACO-RFD hybrid method to solve NP-complete problems. Frontiers of Computer Science, 2013, 7(5): 729–744

    Article  Google Scholar 

  33. Wang Y, Cai Z X. A hybrid multi-swarm particle swarm optimization to solve constrained optimization problems. Frontiers of Computer Science, 2009, 3(1): 38–52

    Article  Google Scholar 

  34. Chen G L, Guo W Z, Chen Y Z. A PSO-based intelligent decision algorithm for VLSI floorplanning. Soft Computing, 2010, 14(12): 1329–1337

    Article  Google Scholar 

  35. Guo W Z, Liu G G, Chen G L, Peng S J. A hybrid multi-objective PSO algorithm with local search strategy for VLSI partitioning. Frontiers of Computer Science, 2014, 8(2): 203–216

    Article  MathSciNet  Google Scholar 

  36. Koh C K, Madden P H. Manhattan or non-manhattan? A study of alternative VLSI routing architectures. In: Proceedings of the 10th Great Lakes symposium on VLSI. 2000, 47–52

    Google Scholar 

  37. Kennedy J, Eberhart R C. A discrete binary version of the particle swarm algorithm. In: Proceedings of the IEEE International Conference on Systems, Man, and Cybernetics. 1997, 4104–4108

    Google Scholar 

  38. Hu X, Eberhart R C, Shi Y. Swarm intelligence for permutation optimization: a case study of n-queens problem. In: Proceedings of Swarm Intelligence Symposium. 2003, 243–246

    Google Scholar 

  39. Parsopoulos K E, Halgamuge M N. Recent approaches to global optimization problems through particle swarm optimization. Natural Computing, 2002, 1(2-3): 235–306

    Article  MathSciNet  MATH  Google Scholar 

  40. Salman A, Ahmad I, Al-Madani S. Particle swarm optimization for task assignment problem. Microprocessors and Microsystems, 2002, 26(8): 363–371

    Article  Google Scholar 

  41. Clerc M. Discrete particle swarm optimizationillustrated by the traveling salesman problem. In: Onwubolu GC, Babu BV: eds. New optimization techniques in engineering. Berlin: Springer-Verlag, 2004: 219–239.

    Chapter  Google Scholar 

  42. Pan Q K, Tasgetiren M F, Liang Y C. A discrete particle swarm optimization algorithm for the permutation flowshop sequecing problem with makespan criteria. In: Proceedings of Research and Development in Intelligent Systems XXIII. 2006, 19–31.

    Google Scholar 

  43. Dietzfelbinger M, Naudts B, van Hoyweghen C, Wegener I. The analysis of a recombinative hill-climber on H-IFF. IEEE Transactions on Evolutionary Computation, 2003, 7(5): 417–423

    Article  Google Scholar 

  44. Qian C, Yu Y, Zhou Z. An analysis on recombination in multi-objective evolutionary optimization, Artificial Intelligence, 2013, 204: 99–119

    Article  MathSciNet  Google Scholar 

  45. Alpert C, Tellez G. The importance of routing congestion analysis. In: Proceedings of the IEEE Design Automation Conference. 2010, 1–14

    Google Scholar 

  46. Shi Y H, Eberhart R C. A modified particle swarm optimizer. In: Proceedings of the IEEE International Conference on Evolutionary Computation. 1998, 69–73

    Google Scholar 

  47. Ratnaweera A, Halgamuge S K, Watson H C. Self-organizing hierarchical particle swarm optimizer with time-varying acceleration coefficients. IEEE Transactions on Evolutionary Computation, 2004, 8(3): 240–255

    Article  Google Scholar 

  48. Lv H, Zheng J, Zhou C, Li K. The convergence analysis of genetic algorithm based on space mating. In: Proceeding of the 5th International Conference on Natural Computation. 2009, 557–562

    Google Scholar 

  49. Rudolph G. Convergence analysis of canonical genetic algorithms. IEEE Transactions on Neural Networks, 1994, 5(1): 96–101

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. College of Mathematics and Computer Science, Fuzhou University, Fuzhou, 350116, China

    Genggeng Liu, Wenzhong Guo, Rongrong Li, Yuzhen Niu & Guolong Chen

  2. Fujian Provincial Key Laboratory of Network Computing and Intelligent Information Processing, Fuzhou University, Fuzhou, 350116, China

    Wenzhong Guo & Guolong Chen

Authors
  1. Genggeng Liu
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  2. Wenzhong Guo
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  3. Rongrong Li
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  4. Yuzhen Niu
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  5. Guolong Chen
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Corresponding author

Correspondence to Wenzhong Guo.

Additional information

Genggeng Liu is a PhD candidate in the College of Mathematics and Computer Science, Fuzhou University, China. His interests include computational intelligence and very large scale integration physical design.

Wenzhong Guo received his BS and MS in Computer Science from Fuzhou University, China in 2000 and 2003, respectively. He received his PhD in communication and information systems from Fuzhou University in 2010. He is currently a full professor with the College of Mathematics and Computer Science at Fuzhou University. His research interests include mobile computing and evolutionary computation. Currently, he leads the Network Computing and Intelligent Information Processing Laboratory, which is a key Laboratory of Fujian Province, China.

Rongrong Li is a MS candidate at the College of Mathematics and Computer Science, Fuzhou University, China. His interests include computational intelligence and very large scale integration physical design.

Yuzhen Niu received her BS and PhD in computer science from Shandong University, China in 2005 and 2010, respectively. She was a post-doctoral researcher with the Department of Computer Science, Portland State University, Portland. She is currently a professor with the College of Mathematics and Computer Science, Fuzhou University, China. Her current research interests include computer graphics, vision, and multimedia.

Guolong Chen received his BS and MS in Computational Mathematics from Fuzhou University, China in 1987 and 1992, respectively, and his PhD in Computer Science from Xi’an Jiaotong University, China in 2002. He is a full professor with the College of Mathematics and Computer Science at Fuzhou University. His research interests include computation intelligence, computer networks, and information security.

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Liu, G., Guo, W., Li, R. et al. XGRouter: high-quality global router in X-architecture with particle swarm optimization. Front. Comput. Sci. 9, 576–594 (2015). https://doi.org/10.1007/s11704-015-4017-1

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